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Analytica Chimica Acta 595 (2007) 198–208

pH- and time-dependent hemoglobin transitions: Acase study for process modelling

Gloria Munoz, Anna de Juan ∗Chemometrics Group, Department of Analytical Chemistry, Universitat de Barcelona,

Diagonal 647, 08028 Barcelona, Spain

Received 17 October 2006; accepted 28 November 2006Available online 10 December 2006

bstract

The study of the pH- and time-dependent transitions of the hemoglobin is presented as a biochemical problem of interest and as a very completexample of the situations that can be encountered in the modelling of complex processes. Therefore, the aim is two-fold: providing a completexplanation of the biochemical phenomena studied and explaining the modelling strategies used to solve this problem that can be generally appliedn processes of different origin. Multivariate curve resolution-alternating least squares (MCR-ALS) is the basic method used to recover the process

ontributions, expressed as the concentration profile and the pure spectrum of each of the compounds involved. What is the benefit of usingultitechnique or multiexperiment data arrangements, how constraints should be selected and applied and how hybrid approaches combining hard-

nd soft-modelling can allow for the use of a partially known model when available are among the main issues presented.2006 Elsevier B.V. All rights reserved.

eywords: Protein processes; Multivariate curve resolution; Process analysis; Hybrid hard- and soft-modelling

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. Introduction

Spectroscopic monitoring is the most common way to fol-ow the development of a process. Process modelling aims atbtaining the process profiles, i.e., the evolution of the concen-ration as a function of the process-driving variable, and the purepectra linked to each constituent in the process from the soleeries of spectra collected [1–5]. Processes can be very diversen terms of the number of components involved, the complexityf their mechanisms and the a priori knowledge or existencef basic principles, e.g., kinetic or physicochemical laws thatan describe the process evolution through mathematical mod-ls [3–5]. The raw measurements linked to a process can varys well and can come from a single technique or be the result of

multitechnique process monitoring [6–9]. Taking as a general

ramework the use of multivariate resolution methods for processodelling, different strategies should be adopted depending on

∗ Corresponding author. Tel.: +34 934039274; fax: +34 934021233.E-mail addresses: anna.dejuan@ub.edu, annaj@apolo.qui.ub.es

A. de Juan).

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he structure of the measurements and on the possibility of usingathematical expressions that can (partially or totally) describe

he process evolution [2,4,5,10].Protein processes are good and challenging examples to show

ost of the situations and possibilities that can be encountered inrocess modelling. Thus, the many events taking place in a pro-ein process often need a multitechnique monitoring to be fullyxplained and the process evolution can be, at most, partiallyescribed by mathematical expressions [11–14].

Proteins are biomacromolecules that are organised intructural levels of increasing complexity: primary structure,econdary structure, tertiary structure and quaternary structurein cases that the protein has more than one subunit to organise)15]. This hierarchical structural system is responsible for theany events that can be observed in a protein process, which

an take place at one or more structural levels.The model protein for this work is the bovine hemoglobin

Hb), which is an alpha-helix heme protein which consists of

tetramer, formed by two alpha and two beta subunits in its

ative form. Each subunit has a different number of aminocids but the same three-dimensional structure. In the tetramer,here are two identical dimers; �2�2 is another tetramer’s

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ame and each globin chain contains a heme group (seeig. 1). The interest of this protein lies on the number andifferent nature of the transitions that can show, linked to vari-tions at different structural levels and to the binding of theeme group to the globin chain or to other ligands, such asxygen.

Protein processes can take place by the addition of denat-rant agents (for example: urea or guanidine hydrochloride)r by the modification of a particular variable, such as T, pHr P. In this case, we focus on the study of pH- and time-ependent protein transitions. The mechanism and the identityf the protein conformations involved in a protein process cane studied by monitoring spectroscopic changes at the differ-nt structural levels [16]. In heme proteins, we can also monitorhanges in the binding of heme group. Thus, circular dichro-sm (CD), UV–vis spectroscopy and fluorescence were usedo study the pH-dependent hemoglobin (Hb) transitions. Flu-rescence (300–450 nm) and near-UV CD (250–350 nm) weresed to monitor changes in the tertiary structure, far-UV CD185–250 nm) in the secondary structure and the CD Soretegion (380–430 nm) to interpret the variation associated withhe heme group. UV spectroscopy (350–700 nm) allowed for the

onitoring of all the structural changes mentioned above. Time-ependent experiments were only studied by UV spectroscopy11–14,16,17].

The results presented in this work have a two-fold aim. Fromhe biochemical point of view, the integral description of theH- and time-dependent transitions of the hemoglobin; from

he process modelling prospect, showing the potential of the

ultitechnique and multiexperiment monitoring and providinguidelines to apply the available data analysis tools to improvehe interpretation and modelling of complex processes.

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mica Acta 595 (2007) 198–208 199

. Experimental procedures

.1. Materials

Bovine hemoglobin was purchased from Sigma and was usedithout prior purification. Ammonia solution 25% a.r., acetic

cid 96% a.r. and ammonium acetate were purchased fromerck. Ammonium chloride 99.5% and hydrochloric acid 37%,

.r., were from Panreac.

.2. Instrumentation

UV spectra were recorded with a Perkin-Elmer �-19 spec-rometer equipped with a Peltier-type thermostatted cell holder.bsorbance lectures were measured from 350 to 700 nm. A 1-

m pathlength cell was used. Scan speed was 240 nm min−1 andhe wavelength step was 0.8 nm.

Fluorescence emission spectra were performed with anminco Bowman AB-2 fluorimeter, equipped with a cell holder

hermostatted by a water circulation bath. Emission spectra wereeasured between 300 and 450 nm. The excitation wavelengthas 280 nm. A 1-cm pathlength cell was used. Scan speed wasnm min−1 and spectra resolution was 1 nm.

CD spectra were obtained using a Jasco spectropolarime-er (model J-720) equipped with a cell holder thermostatted by

water circulation bath. Far-, near-UV and Soret region CDpectra covered 190–250, 250–350 and 380–430 nm wavelengthanges, respectively. The following instrumental settings weresed: scan speed, 100 nm min−1; step resolution 0.5 nm; 1-cmathlength for near-UV CD and Soret region experiments and-mm pathlength for far-UV CD experiments.

The pH meter was a Cyberscan 2500 with a combined pHnd Ag/AgCl Thermo Orion electrode.

.3. Experimental procedure

.3.1. pH-dependent Hb experimentsAll sample solutions were prepared from a stock solution ca.

0−4 M of Hb in water. The sample solutions were prepared byiluting appropriately the 10−4 M Hb solution in 10 mM ammo-ium acetate or 10 mM ammonium chloride. The pH range wasrom 1.5 to 10 approximately. NH3 and HCH3COO or NH3 andCl were added to adjust the pH value.Protein solutions of ca. 10−6 M were used to record UV, flu-

rescence and far-UV circular dichroism spectra. Near-UV CDnd Soret region spectra were measured in ca. 10−5 M proteinolutions.

All sample solutions were measured at 25 ◦C: 2 min wereaited for the stabilisation of the protein solution before record-

ng the spectrum.

.3.2. Time-dependent Hb experimentsThe sample solution was prepared by dilution of the Hb stock

olution 10−4 M in 10 mM ammonium acetate/acetic acid to ab concentration 5× 10−6 M at pH 1.92. This pH value was cho-

en because the only species with significant kinetic evolutions predominant.

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Sample solution was kept at 25 ◦C and a series of spectra wasollected every 30 min for a total period of 48 h.

UV spectroscopy was chosen as the technique to carry outhe kinetic study because this was the only technique giving aistinct spectral signal for the most acidic Hb conformation.

. Data treatment

.1. Data arrangement

The spectra recorded during the monitoring of pH-dependentr time-dependent experiments were organised in a data matrix, whose rows are the spectra collected at each pH value or

t each time and whose columns describe the protein spectro-copic behaviour for each wavelength. This dataset containsll necessary information to describe the protein conformationsnvolved in the process and to identify the structure of all speciesetected.

The data matrix D collected during a protein process can beecomposed according to the Lambert–Beer law following thexpression:

= CST +E

here C and ST are the matrices that contain the concentra-ion profiles of each protein conformation (process profiles) andhe pure spectra, respectively. E is the error matrix. We canork with a single data matrix (two-way data sets) or with row-ise or column-wise augmented data matrices (three-way data

ets). Fig. 2 shows a scheme of these data matrix arrangements.n row-wise or column-wise augmented matrices we need to

ave one direction of the submatrices appended in commonrows or columns, respectively), but the data decomposition fol-ows the same bilinear model as a single data matrix [2,18,19].

ultitechnique data arrangements are examples of row-wise

ig. 2. MCR-ALS data decomposition of: (a) single data matrix. D is a dataatrix of spectra recorded during a process. C are concentration profiles. ST are

ure spectra. (b) Row-wise augmented data matrix. D is a data matrix formedy five submatrices. Di are submatrices recorded during a process by differentpectroscopic techniques. (c) Column-wise augmented data matrix. D is a dataatrix formed by two submatrices Di, related to different experiments monitoredith the same spectroscopic technique.

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mica Acta 595 (2007) 198–208

ugmented matrices, where matrices containing measurementsf different techniques on the same process are appended oneesides the other. The process direction is common (leads tosingle data matrix C) and the data matrix lengthens in the

pectral direction (ST is an augmented matrix). Multiexper-ment data arrangements are examples of column-wise data

atrices, where matrices of different processes sharing com-onents in common are appended one on top of each other.he spectral direction is common (single data matrix ST) and

he data matrix lengthens in the process direction becausehe augmented matrix C contains the evolution of severalrocesses.

.2. General description of multivariate curveesolution-alternating least squares (MCR-ALS)

Within the possible multivariate resolution methods, multi-ariate curve resolution-alternating least squares (MCR-ALS)as applied to resolve the concentration profiles and pure spec-

ra associated with the different pH-induced and time-dependentrotein conformations [2,18,19]. MCR-ALS is a chemometricool that has been used successfully to resolve the protein tran-itions involved in a protein process [11–14] and, in general, toodel processes or evolutionary systems of very diverse nature

2,6–9]. The general steps used in MCR-ALS are:

. Determination of the number of compounds in D (SVD).

. Building initial estimates, C-type (e.g., evolving factor anal-ysis, EFA) [20] or ST-type (e.g., selection of purest spectra,SIMPLISMA [21]).

. Given D and C, constrained least-squares calculation of ST

ST = (CTC)−1

CTD, ST = C +D

. Given D and ST, constrained least-squares calculation of C

C = DS(STS)−1

, C = D(ST)+

. Go to step 3 until convergence is achieved.

The quality of the MCR-ALS model is assessed by differ-nt indicators linked to the correct reproduction of the originalata set through the use of the resolved MCR-ALS model, i.e.,he CST product. These are the lack of fit, estimated with thequation:

ack of fit (%) = 100×√∑

(d∗ij − dij)∑d2ij

here dij is an element of the experimental matrix D and d∗ijhe element of the MCR-ALS reproduced matrix D* and the

ariance explained (r2), calculated as:

2 (%) = 100×∑

d2∗ij∑

d2ij

a Chimica Acta 595 (2007) 198–208 201

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Datamatrix

[Hb] pH range Number ofspectra

Spectrometrictechnique

D1 1.05× 10−6 M 1.51–10.05 28 Far-UV CDD2 9.94× 10−6 M 1.98–9.92 26 Near-UV CDD 9.94× 10−6 M 1.98–9.92 26 CD Soret regionDD

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We also add the standard deviation of the residuals, σ,hich should be similar to the error linked to the experimentaleasurements

=√∑

(d∗ij − dij)2

n

here n is the number of elements in the data set.In any iterative method, the appropriate application of con-

traints is crucial to drive the optimisation to the right solution. Aonstraint forces a profile to be shaped so as it fulfils a systematiceature in the dataset, either mathematical or chemical [2,18,22].elow, the most generally used constraints in a (protein) processre described.

Non-negativity: this constraint is the most used in resolutionethods and prevents the presence of negative values in profiles.

t is applied to concentration profiles and to UV–vis and fluo-escence spectra because their absorbance/fluorescent intensitiesre always positive.

Unimodality: this constraint forces the only presence of oneaximum in a species profile. This is applied to processes,here the concentration profiles show an emergence-decay

hape.Closure: this constraint is applied when the total concen-

ration of all detectable species in each stage of a process isonstant. When there are non-absorbing species in the system,e cannot apply this constraint because the species contributing

o the measured signal do not form a closed system.Local rank/selectivity: this constraint imposes absence of

ome species in a specific range of the concentration profiles,.e., in certain pH or time windows. This knowledge can havechemical basis or be acquired by applying local rank analysisethods [20].Hard-modelling: this constraint is applied when the chem-

cal law (kinetic or thermodynamic) linked to a particularrocess is known. The concentration profiles linked to compo-ents in the process are forced to present the shape describedy the chemical law [10,23,24]. In protein processes, thisonstraint has been applied to the time-dependent experi-ents.A general feature of all constraints is that they can be applied

o one or more species within an experiment and to one or moreand/or ST submatrices in augmented matrix arrangements.

his flexibility makes the method adaptable to the properties ofach particular process/measurement.

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able 2CR-ALS results obtained after the analysis of the single data matrices

xperiment Spectrometrictechnique

Number ofabsorbing species

pH crossing pointconformational tr

Far-UV CD 2 4.0Near-UV CD 2 4.5CD Soret region 2 7.8Fluorescence 3 4.2/8.7UV 4 2.8/3.9/8.5

3

4 2.15× 10−6 M 2.51–10.09 25 Fluorescence

5 2.22× 10−6 M 2.50–9.96 25 UV

. Results and discussion

.1. Description of hemoglobin pH-dependent transitionsmultitechnique process monitoring)

.1.1. Individual analysis of experimentsEven though the ultimate goal in multitechnique monitored

rocesses is the global analysis of all measurements, it is alwaysorth starting by the individual analysis of each kind of mea-

urement to detect mismatches in the process description (due toeal chemical reasons, to differences in the phenomena detectedy the different techniques or, simply, to errors in the measure-ent step) or to have a separate view on particular aspects of the

rocess of interest.In our example, the study of hemoglobin at different pH

alues with several spectroscopic techniques gives informationbout the different conformations that the protein can adoptn acidic, neutral or basic pH. Table 1 shows the experimentserformed and the working conditions. First of all, series ofpectra obtained in each technique (circular dichroism, fluores-ence and UV) were individually analysed by MCR-ALS. Theata analysis procedure, adapted to the kind of measurementsnd transitions studied, and the results obtained are commentedn next subsections. Quality parameters related to the fit qualityf the analyses performed are shown in Table 2.

.1.1.1. Circular dichroism. CD experiments in the differentpectral regions were sensitive to different events of the proteinrocess [17,25]. In all circular dichroism regions, the spec-ra were unconstrained because of the natural occurrence ofegative ellipticities in this technique. Constraints in the con-entration direction varied according to the transitions detected

nd to the properties of the process components involved.

4.1.1.1.1. Far-UV CD (198–250 nm). This spectral regions specifically sensitive to changes in the secondary structure ofroteins. Fig. 3A shows the raw data collected during experiment

s inansitions

Fit quality

Sigma (σ) Lack of fit (%) Variance explained (%)

0.393 4.97 99.750.588 24.87 93.830.272 4.78 99.770.001 1.75 99.960.012 5.03 99.75

202 G. Munoz, A. de Juan / Analytica Chimica Acta 595 (2007) 198–208

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ig. 3. Spectra collected during pH-dependent experiments of hemoglobin. (Aluorescence spectra. (E) UV absorption spectra.

1. SVD analysis detected two components. In the resolution ofhe data set, the concentration profiles have been constrainedo be non-negative, unimodal and to form a closed system.ig. 4A shows the concentration profiles and spectra linked to

he native and denatured forms of secondary structure. As cane observed, denaturation (loss of the native structure presentt neutral pH values) starts to be important at pH values lowerhan 4. The spectrum obtained for the native structure shows theypical spectral features described for an alpha-helix motif, i.e.,n intense negative band with two shoulders located at 220 and10 nm, approximately [26]. The denatured structure has a neg-tive band at shorter wavelengths and weaker features around20 nm, typical from random coil conformations.

4.1.1.1.2. Near-UV CD (250–350 nm). This zone respondso the environment of aromatic residues, which is representativef the protein tertiary structure (see raw spectra of experiment2 in Fig. 3B). SVD analysis detected two components. The

oncentration profiles have been constrained as in the far-UVD region. Fig. 4B shows the resolved concentration profiles and

pectra. Denaturation starts to be important at pH values lowerhan 4.5. The resolved spectra show a species with a disorganizedertiary structure (solid line) and an organized tertiary structuredotted line). The organized structure (N) shows a spectrum withn intense positive band around 260 nm, typical from aromatichromophores when they are in a globular structure [27]. The

isorganized tertiary structure (D) shows an almost null signal28,29]. The lack of fit (%) is unusually big, but only two specieshowed distinct enough spectral features that could be modelledith a single data analysis.

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-UV CD spectra. (B) Near-UV CD spectra. (C) Soret region CD spectra. (D)

4.1.1.1.3. Soret region in CD (380–430 nm). This region isinked to variations associated with the heme group (binding ofhe heme group to the globin and binding of the heme group to thexygen) (see Fig. 3C for raw data of experiment D3) [17]. SVDnalysis indicates the presence of two absorbing species. Theoncentration profiles have been constrained to be non-negativend unimodal. The closure constraint is not applied because theotal concentration of all absorbing species in this spectral ranges not constant along the whole pH range. Actually, it is knownhat the heme group, when unbound from the globin, does notive any signal in the Soret region and, hence, the related species,hough present, cannot be modelled from the sole spectroscopic

easurement [30].Fig. 4C shows the resolved profiles. The concentration pro-

les show two absorbing species with the heme group linked tohe globin, presumably the native deoxyhemoglobin at lower pHalues (T state or tense form) and the oxyhemoglobin at higherH values (R state or relaxed form). The resolved spectra con-rm the tense→ relaxed (T→R) transition when pH goes fromto 10 approximately. The O2-heme binding and the different

rientation of the heme group when bound to O2 results in aed shift in the protein spectrum [28,31,32]. At pH < 4, theres an apparent lack of protein in the system (null concentrationalues). This fact matches the well-known lack of signal of therosthetic group when is not linked to the protein and the lack of

ntrinsic signal of the heme group and the globin in this spectralange (noticeable also in the first raw spectra in Fig. 3C). Thus,he third chemical species in the system, linked to the denaturedlobin after the loss of the heme group, although present, can-

G. Munoz, A. de Juan / Analytica Chimica Acta 595 (2007) 198–208 203

Fig. 4. Concentration profiles and spectra from MCR-ALS individual resolution of pH-dependent Hb experiments. (A) Far-UV CD results. Native secondary structureis shown by a solid black line and denatured secondary structure is shown by a dotted black line. Circles and squares are experimental points, respectively. (B)Near-UV CD. Disorganized tertiary structure is shown with a solid black line and organized tertiary structure with a dotted black line. (C) Soret region. Native form(T) is represented by a solid black line and the conformation at basic pH (R) by a dotted black line. (D) Fluorescence. Native form is represented by a dotted blackl t basii solidb

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ine. The acidic form is represented by a solid black line and the conformation as represented by a dashed black line. The most acidic form is represented by aasic form is represented by a solid black thin line.

ot be explicitly modelled from the individual analysis of thispectral region.

.1.1.2. Fluorescence. Fluorescence is a spectral techniqueainly sensitive to changes in the tertiary structure of proteins

see raw spectra from experiment D4 in Fig. 3D) [33]. Fluores-ence spectra have been normalised to suppress random intensityhanges unrelated to the monitored process [11]. SVD detectedhree fluorescent species. The concentration profiles have beenonstrained to be non-negative, unimodal and closed. The spec-ra have been constrained to be non-negative. Fig. 4D showshree concentration profiles with two different pH crossing val-es between species. The lowest pH crossing value agrees withhe experiments using far- and near-CD and the highest pH cross-ng value with the experiment in the Soret CD experiment. The

ative form is represented by a dotted line and extends aroundhe physiological neutral pH value, the other two forms are moreisordered than the native form, they appear at most extreme pHalues and their pure spectra are red shifted with respect to the

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c pH by a dashed black line. (E) UV absorption spectroscopy. Native structureblack thick line and the other acidic conformation by a dotted black line. The

ative form [11]. Within the non-native forms, the acidic forms the most disordered because it is the most red-shifted.

.1.1.3. UV absorption spectroscopy. UV absorption is sensi-ive to changes in secondary and tertiary structure of the proteinnd in the configuration of the heme group (see raw spectra ofxperiment D5 in Fig. 3E). SVD analysis detected four com-onents. Fig. 4E contains the resolution results. Concentrationrofiles and spectra have been constrained as fluorescent data.he concentration profiles indicate the presence of two acidicpecies, one basic species and the native structure at physiolog-cal pH. Spectra show that the dominant species at pH > 8 is thexyhemoglobin, as can be seen from the oxygen peaks at 541nd 576 nm, typical from the oxygen bound to the heme group34]. The two acidic species correspond to denaturated forms of

he protein: the first, appearing around pH 4, shows a clear lossf spectral intensity with respect to the native form, whereas theost acidic one, only detected by molecular UV absorption, hasdistinct and more intense spectrum.

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.1.2. Global analysis of experimentsBefore carrying out a global analysis of several experiments,

t is worth observing and comparing the results obtained in thendividual analyses, shown in Table 2. Different techniques maye sensitive to different phenomena and may show complemen-ary information, but there are always systematic trends in thendividual analyses that should also appear in the global analysisf all measurements.

Looking at the hemoglobin results in Table 2, we can observewo consistent pH crossing values, the first at pH≈ 4, identifieds the denatured← native transition and the second, at pH≈ 8,s the deoxyhb(native)→ oxyHb transition. These crossingoints are detectable with some of the techniques used. We canlso detect another pH crossing value at lower pH values, onlybserved by UV spectroscopy. The reasons why several tech-iques can provide different results are very diverse. From ahemical point of view, the complexity of the events of a pro-ein process at different structural levels can be different and,herefore, techniques sensitive to particular protein levels willot necessarily ‘notice’ the same transitions. From the datanalysis prospect, non-absorbing species cannot be modelledith an individual analysis and, as a consequence, the tran-

itions where they participate either. Another typical problemccurs when different species in a process show an identi-al spectral shape, e.g., they only differ in intensity; then, thendividual analysis cannot recognise them as separate contri-utions (rank-deficiency phenomenon in the spectral direction35,36]).

To improve the results of the individual analyses and to obtain

more accurate and robust description of the global process,e analyse simultaneously all the data sets shown before. Toerform the global analysis, a row-wise augmented data matrix isuilt with the matrices of the different techniques appended one e

ig. 5. Concentration profiles and spectra obtained in the multitechnique global analine. The conformation at basic pH is represented by a solid grey line. Two acidic con

mica Acta 595 (2007) 198–208

ext to the other (see Fig. 2b). In this matrix, there is a commonrocess direction (C profiles) and a row-wise augmented matrixith the resolved spectra of the different techniques analysed

imultaneously.SVD analysis of the global data set detected four compo-

ents. Constraints applied to the C matrix are non-negativity,nimodality and closure. Note that some limitations in the usef constraints in the individual analysis are overcome, e.g., clo-ure could not be applied to the Soret CD spectra because ofhe presence of a non-absorbing species. Now, the augmentedpectrum of this species, although having a non-absorbing zone,rovides a non-null global contribution to the signal. Constraintspplied to each ST

i submatrix are those described in the relatedechnique data analysis.

Fig. 5 shows the concentration profiles and the spectrabtained in the global analysis. The lack of fit of the globalnalysis is 9.16% and the variance explained 99.16%. The con-entration profiles show two acidic conformations (denatured),neutral conformation (native protein) and a basic conformation

oxyHb). The pH crossing points among species agree with thoseuggested in Table 2 and confirm the main transitions found withhe individual analyses (see scheme below).

The native form is represented by a dotted grey line andxtends from pH≈ 4 to pH≈ 8. From the spectral shapes

ysis of pH-dependent experiments. Native form is represented by a dotted greyformations are represented by a solid black line and a dotted black line.

G. Munoz, A. de Juan / Analytica Chimica Acta 595 (2007) 198–208 205

Fig. 6. Results of studying the ageing solution effect on pH-dependent UV absorption experiments. (A) Individual resolution of fresh protein samples. (B) Individualr

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esolved, it can be seen that it has secondary and tertiary struc-ures ordered and the heme group bound. The conformation atasic pH, represented by a solid grey line, has a heme coordina-ion different from the native structure because it is red-shiftedn the Soret CD region and is bound to oxygen, as shown in theeatures of the UV absorption spectrum. This oxyhemoglobinpecies shows a native-like secondary structure (see far-UV CDpectrum) and a modified tertiary structure, as can be seen nown the near-UV CD spectrum, significantly more intense than forhe native form.

Two acidic conformations are represented by a solid blackine and a dotted black line. They have a complete disorderedertiary structure because of the practically null near-UV CDpectrum and disordered secondary structure (decrease of the20 nm band at the far-UV CD spectrum). The loss of the hemeroup is now seen through the null signal at the Soret region.he UV spectra confirm that these two disordered species areot identical.

Going back to the process modelling prospect, we willxamine some of the differences and benefits provided by thelobal analysis with respect to the individual analyses. A cru-ial point is the robustness in the process description, providedy the fact that the only set of process profiles is representa-

ive of the variation measured by all spectroscopic techniques.nother essential issue is the possibility of recovering species

hat could not be modelled in an individual analysis. Two dif-erent examples of this kind are encountered in the hemoglobin

wct(

ystem. The first refers to the recovery of resolved null spec-ra for a particular technique, such as those of the denaturedorms of the protein when monitored with CD Soret mea-urements (compare Fig. 4C, individual analysis, and Fig. 5).orking with a matrix of augmented spectra makes that null

pectra (in the Si submatrix of CD Soret spectra) can nowe explicitly recovered because they are parts of longer non-ull augmented spectra (the augmented S matrix). The secondxample illustrates the possibility of recovering species withdentical spectral shape and only differing in intensity, such ashe near-UV CD resolved spectra of native hemoglobin andxyhemoglobin. In this case, working with an augmented Satrix breaks the rank-deficiency in the spectral direction, i.e.,

he spectra of these two species have identical shape accordingo the near-UV CD measurements and cannot be distinguishedf no other information is present (see Fig. 4C), but this equalhape does not extend to all the techniques in the longer aug-ented spectra and they can be modelled separately in the

ugmented S matrix (see spectra of the near-UV CD Si sub-atrix in Fig. 5). At this point, it is important to note that

lobal analysis does not create artificial differences amongpecies when they do not naturally exist. Thus, looking at thear-UV CD spectra recovered in the global analysis (Fig. 5),

e see that the four resolved spectra are pairwise identical,

onfirming the presence of only one important transition athis protein structural level, as found in the individual analysissee Fig. 4A).

2 a Chimica Acta 595 (2007) 198–208

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.2. Description of hemoglobin time-dependent transitions

.2.1. pH-dependent experiments performed at differentimes

Processes are often subject to variations caused by exter-al factors. When these variations cannot be avoided or keptnder control, they should be taken into account in the processodelling.In the hemoglobin example, we were interested in knowing

he protein solution ageing effect on the pH-dependent transi-ions found. To do so, a series of UV spectra were recordedn protein samples at different pH values in the fresh solutionsnd after 24 h. UV spectroscopy was chosen because it was thenly technique that showed distinct spectra for the four involvedrotein conformations.

Fig. 6 shows the resolved concentration profiles and spec-ra obtained from the individual analysis of the experimentserformed in the two consecutive days.

Whereas the evolution of the process profiles is very similar inhe two experiments, the recovered spectra show an importantecrease in absorption intensity in the most acidic species, atH≈ 2. Since both data sets were collected on the same samplesnd were measured in the same experimental conditions, therotein solution ageing appears as the main reason for the signalariation. This spectral change with time was only significantor the most acidic species and, therefore, we decided to do aime-dependent experiment at pH≈ 2.

.2.2. Time-dependent experiment at pH 1.92Fig. 7A shows a series of spectra collected every 30 min for

period of 48 h in a hemoglobin solution at pH 1.92.SVD analysis detected two components. MCR-ALS with a

ard modelling constraint was applied to resolve the kineticxperiment. The concentration profiles were constrained to beon-negative, unimodal, closed and to follow a first order reac-

ion with an Ak1−→B kinetic model. Using a hard-modelling

onstraint, the rate constant of the process can be obtained andhe concentration profiles are unique. Fig. 7B shows concentra-ion profiles and spectra from the MCR-ALS hard-modelling.

Results obtained show that the kinetic model (Ak1−→B)

as correct to describe the data evolution. The lack of fit is%) 1.35%, the variance explained 99.98%, sigma 0.004 and1 = 1.38× 10−5 s−1.

.3. Global model of time- and pH-dependent Hbransitions

Since the solution ageing effect was seen to be significant inhe species involved in the pH-dependent transitions, a globalnalysis including pH- and time-dependent experiments waseeded to give a reliable picture of the hemoglobin system.

To carry out a complete description of the process, we workedith a column-wise augmented matrix (see Fig. 2c), formed by aH-dependent experiment performed on samples measured after4 h and a time-dependent experiment at pH 1.92.

dtmb

ig. 7. MCR-ALS resolution of a time-dependent experiment with a hard-odelling constraint. (A) Raw data. (B) Concentration profiles. (C) Resolved

pectra.

SVD analysis detected five components. MCR-ALS withard modelling constraint was applied. The UV spectra in theingle matrix S were constrained to be non-negative and theoncentration profiles in the Ci submatrices of the column-ise augmented C matrix were constrained according to the

haracteristics of the related experiment. Thus, the concentra-ion profiles in the pH-dependent experiment were constrainedo be non-negative, unimodal, closed and to obey some localank conditions (see Section 3.2), whereas the hard mod-lling constraint incorporating a first order kinetic model wassed only in the time-dependent C submatrix. This is a main

ifference with classical hard-modelling methods, where allhe variation measured in the system should respond to a

odel. Using the hard-model as an additional constraint, it cane applied in a partial way and only affect the experiments

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r the species that are known to obey the related chemicalehaviour.

Another constraint, typical in multiexperiment data analy-is, was applied. It is known as the correspondence among thepecies in the experiments. It consists of building a matrix (isp),ized (nr. of experiments× nr. of species) where the absencend presence of species is coded in a binary form, i.e., 1 forresent species and 0 for absent species. This presence/absencenformation will be kept in the modelled process profiles. In theemoglobin system, this matrix will have the following form:

nd the sequence of the species would be from acid to basic.hus, in the pH-dependent experiment, there will be fivepecies, whereas in the time-dependent experiment, only the

ig. 8. MCR-ALS global model of time- and pH-dependent hemoglobin tran-itions. (A) Kinetic profiles obtained using a hard-modelling constraint. (B)H-dependent concentration profiles. (C) Resolved spectra.

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mica Acta 595 (2007) 198–208 207

wo most acidic species should present non-null concentrationrofiles.

Fig. 8 shows the resolved concentration profiles forach submatrix and the related spectra. Results are: lackf fit = 3.29%, variance explained = 99.89%, σ = 0.011 and1 = 1.41× 10−5 s−1. We can observe that k1 agrees with thealue obtained in Section 4.2.2 with the individual analysis. Theesolved spectra keep the form expected in the individual anal-sis of the time- and pH-dependent experiments (see Fig. 8C)nd the concentration profiles of the time-dependent experimentgree with those found in the individual analysis (see Fig. 8A).he main difference is in the concentration profiles linked to

he pH-dependent experiment in Fig. 8B, which shows now fivepecies instead of the four found when the ageing effect wasot taken into account. The incorporation of this fifth speciesccounts for the kinetic behaviour of the most acidic contribu-ion, not described until the pH- and time-dependent experimentsere treated together.Looking at the results obtained, the same benefit found in

he global analysis in Section 4.1.2 is found. Thus, the twoinetic forms that coexist at the most acidic pH values present anvolution as a function of pH almost identical (equally shapedoncentration profiles). This is the reason why they cannote distinguished when the sole pH-dependent experiment isnalyzed. It is an example of rank-deficiency, now in the concen-ration direction. As soon as the two experiments are appended,he augmented concentration profiles of these two species are noonger identical because of the difference in the time-dependentrocess and, therefore, they can be modelled separately.

. Conclusions

This work showed clearly the power of the multitechniquend multiexperiment data analysis for the proper descriptionf complex processes. It provided also an example of applica-ion of hybrid methodologies that allow for combining hard-nd soft-modelling. This strategy allows for using all possi-le information about the model driving a process, even if its partial.

In our example, the use of all these strategies allowedor a global description of the pH-dependent transitions ofemoglobin and of their time-dependency. As a result, fivepecies were characterised and modelled. Three of them, theative hemoglobin, the oxyhemoglobin and the first denaturedpecies did not present a significant evolution as a function ofime. At the most acidic pH values, two species coexisted thatresented a kinetic evolution described by a first-order reactionaw. Only the analysis of a multiexperiment data set by means ofhybrid approach combining soft-modelling (for the pH-depen-ent experiment) and hard-modelling (for the time-dependentxperiment) provided the global picture of the process studied.

eferences

[1] A. de Juan, E. Casassas, R. Tauler, ‘Soft Modeling of Analytical Data’.Encyclopedia of Analytical Chemistry: Instrumentation and Applications,Wiley, 2000, p. 9800.

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[2] A. de Juan, R. Tauler, Anal. Chim. Acta 500 (2003) 195.[3] H. Mauser, G. Gauglitz, Chemical Kinetics, Elsevier, Amsterdam, 1998.[4] M. Maeder, A.D. Zuberbuhler, Anal. Chem. 62 (1990) 2220.[5] G. Puxty, M. Maeder, K. Hungerbuhler, Chemom. Intell. Lab. Syst. 81

(2006) 149.[6] R. Tauler, B. Kowalski, B.S. Fleming, Anal. Chem. 65 (1993) 2040.[7] J. Jaumot, R. Eritja, R. Tauler, R. Gargallo, Nucleic Acids Res. 34 (2006)

206.[8] M. Garrido, I. Lazaro, M.S. Larrechi, F.X. Rius, Anal. Chim. Acta 5 (2004)

65.[9] C.B. Zachariassen, J. Larsen, F. van den Berg, R. Bro, A. de Juan, R. Tauler,

Chemom. Intell. Lab. Syst. 83 (1) (2006) 13.10] A. de Juan, M. Maeder, M. Martınez, R. Tauler, Chemom. Intell. Lab. Syst.

54 (2000) 123.11] S. Navea, A. de Juan, R. Tauler, Anal. Chem. 74 (2002) 6031.12] A. Borges, R. Tauler, A. de Juan, Anal. Chim. Acta 544 (2005) 159.13] S. Navea, A. de Juan, R. Tauler, Anal. Chem. 75 (2003) 5592.14] S. Navea, R. Tauler, A. de Juan, Anal. Chem. 78 (14) (2006) 4768.15] D. Voet, J.G. Voet, Bioquımica, Ediciones Omega, 1992.16] T.E. Creighton, Proteins: Structures and Molecular Properties, W.H. Free-

man and Company, New York, 1993.

17] N. Berova, K. Nakanishi, R.W. Woody, Circular Dichroism. Principles and

Applications, Wiley, NY, 2000.18] R. Tauler, Chemom. Intell. Lab. Syst. 30 (1) (1995) 133.19] J. Jaumot, R. Gargallo, A. de Juan, R. Tauler, Chemom. Intell. Lab. Syst.

76 (2005) 101.

[[

[

mica Acta 595 (2007) 198–208

20] M. Maeder, A.D. Zuberbuhler, Anal. Chim. Acta 181 (1986) 287.21] W. Windig, J. Guilment, Anal. Chem. 63 (1991) 1425.22] A. de Juan, Y. Vander Heyden, R. Tauler, D.L. Massart, Anal. Chim. Acta

346 (1997) 307.23] J. Diewok, A. de Juan, M. Maeder, R. Tauler, B. Lendl, Anal. Chem. 75

(2003) 641.24] J.M. Amigo, A. de Juan, J. Coello, S. Maspoch, Anal. Chim. Acta 567 (2)

(2006) 245.25] A. Rodger, B. Norden, Circular Dichroism and Linear Dichroism, Oxford

University Press, Oxford, 1997.26] J.T. Pelton, L. McLean, Spectroscopic methods for analysis of protein

secondary structure, Anal. Biochem. 277 (2) (2000) 167.27] S.M. Kelly, N.C. Price, Biochim. Biophys. Acta 1338 (1997) 161.28] R. Gabbianelli, G. Zolese, E. Bertoli, G. Falcioni, Eur. J. Biochem. 271

(2004) 1971.29] M.F. Perutz, J.E. Ladner, S.R. Simon, C. Ho, Biochemistry 13 (1994) 2163.30] M.C. Hsu, R.W. Woody, J. Am. Chem. Soc. 93 (14) (1970) 3515.31] C. Zentz, S. Pin, B. Alpert, Methods Enzymol. 232 (1994) 247.32] G. Blauer, N. Sreerama, R.W. Woody, Biochemistry 32 (1993) 6674.33] T.E. Creighton, Protein Structure a Practical Approach, IRL Press at Oxford

University Press, 1989.

34] H.G. Kristinsson, J. Agric. Food Chem. 50 (2002) 7669.35] M. Amrhein, B. Srinivasan, D. Bonvin, M.M. Schumacher, Chemom. Intell.

Lab. Sys. 33 (1996) 17.36] A. Izquierdo-Ridorsa, J. Saurina, S. Hernandez-Cassou, R. Tauler,

Chemom. Intell. Lab. Syst. 38 (1997) 183.